LMFDB - Embedded newform 252.4.x.a.41.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			41.19
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.19

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +O(q^{10})$	\(q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +(7.40072 - 4.27281i) q^{11} +(45.3367 + 26.1752i) q^{13} +(5.08588 + 36.3774i) q^{15} -38.9547 q^{17} +66.4008i q^{19} +(85.1039 + 44.9258i) q^{21} +(173.899 + 100.401i) q^{23} +(37.5151 + 64.9781i) q^{25} +(-56.7874 - 128.289i) q^{27} +(52.9622 - 30.5777i) q^{29} +(-116.401 - 67.2041i) q^{31} +(16.6637 - 41.1590i) q^{33} +(-130.251 - 13.2032i) q^{35} +298.967 q^{37} +(269.400 - 37.6645i) q^{39} +(221.278 - 383.265i) q^{41} +(26.1371 + 45.2708i) q^{43} +(137.104 + 132.780i) q^{45} +(-137.682 - 238.472i) q^{47} +(-227.620 + 256.589i) q^{49} +(-159.594 + 124.504i) q^{51} +136.637i q^{53} +60.4084i q^{55} +(212.226 + 272.039i) q^{57} +(-191.268 + 331.286i) q^{59} +(-261.714 + 151.100i) q^{61} +(492.253 - 87.9458i) q^{63} +(-320.482 + 185.030i) q^{65} +(318.940 - 552.420i) q^{67} +(1033.34 - 144.470i) q^{69} -228.249i q^{71} +1241.68i q^{73} +(361.375 + 146.307i) q^{75} +(128.384 + 92.5530i) q^{77} +(-100.694 - 174.407i) q^{79} +(-642.683 - 344.092i) q^{81} +(-323.452 - 560.235i) q^{83} +(137.684 - 238.476i) q^{85} +(119.251 - 294.549i) q^{87} -826.042 q^{89} +(-97.7786 + 964.598i) q^{91} +(-691.679 + 96.7027i) q^{93} +(-406.497 - 234.691i) q^{95} +(17.0700 - 9.85534i) q^{97} +(-63.2797 - 221.885i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	4.09692	−	3.19613i	0.788453	−	0.615096i
$3$	4.09692	−	3.19613i	0.788453	−	0.615096i
$4$		0			0
$5$	−3.53447	+	6.12188i	−0.316132	+	0.547557i	−0.979678	−	0.200579i	$-0.935718\pi$
$5$	−3.53447	+	6.12188i	−0.316132	+	0.547557i	0.663545	+	0.748136i	$0.269051\pi$
$6$		0			0
$7$	7.59538	+	16.8911i	0.410112	+	0.912035i
$7$	7.59538	+	16.8911i	0.410112	+	0.912035i
$8$		0			0
$9$	6.56950	−	26.1886i	0.243315	−	0.969947i
$10$		0			0
$11$	7.40072	−	4.27281i	0.202855	−	0.117118i	−0.395132	−	0.918625i	$-0.629301\pi$
$11$	7.40072	−	4.27281i	0.202855	−	0.117118i	0.597986	+	0.801506i	$0.295968\pi$
$12$		0			0
$13$	45.3367	+	26.1752i	0.967241	+	0.558437i	0.898394	−	0.439190i	$-0.144735\pi$
$13$	45.3367	+	26.1752i	0.967241	+	0.558437i	0.0688473	+	0.997627i	$0.478068\pi$
$14$		0			0
$15$	5.08588	+	36.3774i	0.0875447	+	0.626174i
$16$		0			0
$17$	−38.9547			−0.555759			−0.277879	−	0.960616i	$-0.589632\pi$
$17$	−38.9547			−0.555759			−0.277879	+	0.960616i	$0.589632\pi$
$18$		0			0
$19$			66.4008i			0.801757i	0.916131	+	0.400879i	$0.131295\pi$
$19$			66.4008i			0.801757i	−0.916131	+	0.400879i	$0.868705\pi$
$20$		0			0
$21$	85.1039	+	44.9258i	0.884343	+	0.466839i
$22$		0			0
$23$	173.899	+	100.401i	1.57654	+	0.910217i	0.995337	+	0.0964590i	$0.0307517\pi$
$23$	173.899	+	100.401i	1.57654	+	0.910217i	0.581204	+	0.813758i	$0.302582\pi$
$24$		0			0
$25$	37.5151	+	64.9781i	0.300121	+	0.519824i
$26$		0			0
$27$	−56.7874	−	128.289i	−0.404768	−	0.914419i
$28$		0			0
$29$	52.9622	−	30.5777i	0.339132	−	0.195798i	−0.320756	−	0.947162i	$-0.603937\pi$
$29$	52.9622	−	30.5777i	0.339132	−	0.195798i	0.659888	+	0.751364i	$0.270604\pi$
$30$		0			0
$31$	−116.401	−	67.2041i	−0.674395	−	0.389362i	0.123345	−	0.992364i	$-0.460638\pi$
$31$	−116.401	−	67.2041i	−0.674395	−	0.389362i	−0.797740	+	0.603002i	$0.793971\pi$
$32$		0			0
$33$	16.6637	−	41.1590i	0.0879024	−	0.217117i
$34$		0			0
$35$	−130.251	−	13.2032i	−0.629041	−	0.0637641i
$36$		0			0
$37$	298.967			1.32838			0.664188	−	0.747565i	$-0.268777\pi$
$37$	298.967			1.32838			0.664188	+	0.747565i	$0.268777\pi$
$38$		0			0
$39$	269.400	−	37.6645i	1.10612	−	0.154645i
$40$		0			0
$41$	221.278	−	383.265i	0.842874	−	1.45990i	−0.0445802	−	0.999006i	$-0.514195\pi$
$41$	221.278	−	383.265i	0.842874	−	1.45990i	0.887455	−	0.460895i	$-0.152472\pi$
$42$		0			0
$43$	26.1371	+	45.2708i	0.0926947	+	0.160552i	0.908644	−	0.417571i	$-0.137119\pi$
$43$	26.1371	+	45.2708i	0.0926947	+	0.160552i	−0.815949	+	0.578123i	$0.803785\pi$
$44$		0			0
$45$	137.104	+	132.780i	0.454182	+	0.439861i
$46$		0			0
$47$	−137.682	−	238.472i	−0.427298	−	0.740101i	0.569334	−	0.822106i	$-0.307201\pi$
$47$	−137.682	−	238.472i	−0.427298	−	0.740101i	−0.996632	+	0.0820049i	$0.973868\pi$
$48$		0			0
$49$	−227.620	+	256.589i	−0.663617	+	0.748073i
$50$		0			0
$51$	−159.594	+	124.504i	−0.438189	+	0.341845i
$52$		0			0
$53$			136.637i			0.354123i	0.984200	+	0.177061i	$0.0566591\pi$
$53$			136.637i			0.354123i	−0.984200	+	0.177061i	$0.943341\pi$
$54$		0			0
$55$			60.4084i			0.148099i
$56$		0			0
$57$	212.226	+	272.039i	0.493157	+	0.632147i
$58$		0			0
$59$	−191.268	+	331.286i	−0.422051	+	0.731014i	−0.996140	−	0.0877790i	$-0.972023\pi$
$59$	−191.268	+	331.286i	−0.422051	+	0.731014i	0.574089	+	0.818793i	$0.305356\pi$
$60$		0			0
$61$	−261.714	+	151.100i	−0.549328	+	0.317155i	−0.748851	−	0.662739i	$-0.769394\pi$
$61$	−261.714	+	151.100i	−0.549328	+	0.317155i	0.199523	+	0.979893i	$0.436061\pi$
$62$		0			0
$63$	492.253	−	87.9458i	0.984412	−	0.175875i
$64$		0			0
$65$	−320.482	+	185.030i	−0.611552	+	0.353080i
$66$		0			0
$67$	318.940	−	552.420i	0.581563	−	1.00730i	−0.413732	−	0.910399i	$-0.635775\pi$
$67$	318.940	−	552.420i	0.581563	−	1.00730i	0.995294	−	0.0968972i	$-0.0308918\pi$
$68$		0			0
$69$	1033.34	−	144.470i	1.80290	−	0.252061i
$70$		0			0
$71$		−	228.249i		−	0.381524i	−0.981636	−	0.190762i	$-0.938904\pi$
$71$		−	228.249i		−	0.381524i	0.981636	−	0.190762i	$-0.0610959\pi$
$72$		0			0
$73$			1241.68i			1.99079i	0.0958607	+	0.995395i	$0.469440\pi$
$73$			1241.68i			1.99079i	−0.0958607	+	0.995395i	$0.530560\pi$
$74$		0			0
$75$	361.375	+	146.307i	0.556373	+	0.225254i
$76$		0			0
$77$	128.384	+	92.5530i	0.190009	+	0.136979i
$78$		0			0
$79$	−100.694	−	174.407i	−0.143404	−	0.248383i	0.785372	−	0.619024i	$-0.212472\pi$
$79$	−100.694	−	174.407i	−0.143404	−	0.248383i	−0.928776	+	0.370641i	$0.879138\pi$
$80$		0			0
$81$	−642.683	−	344.092i	−0.881596	−	0.472005i
$82$		0			0
$83$	−323.452	−	560.235i	−0.427752	−	0.740889i	0.568921	−	0.822392i	$-0.307361\pi$
$83$	−323.452	−	560.235i	−0.427752	−	0.740889i	−0.996673	+	0.0815036i	$0.974028\pi$
$84$		0			0
$85$	137.684	−	238.476i	0.175693	−	0.304310i
$86$		0			0
$87$	119.251	−	294.549i	0.146955	−	0.362976i
$88$		0			0
$89$	−826.042			−0.983824			−0.491912	−	0.870645i	$-0.663702\pi$
$89$	−826.042			−0.983824			−0.491912	+	0.870645i	$0.663702\pi$
$90$		0			0
$91$	−97.7786	+	964.598i	−0.112637	+	1.11118i
$92$		0			0
$93$	−691.679	+	96.7027i	−0.771223	+	0.107824i
$94$		0			0
$95$	−406.497	−	234.691i	−0.439008	−	0.253461i
$96$		0			0
$97$	17.0700	−	9.85534i	0.0178679	−	0.0103161i	−0.491039	−	0.871137i	$-0.663383\pi$
$97$	17.0700	−	9.85534i	0.0178679	−	0.0103161i	0.508907	+	0.860821i	$0.330050\pi$
$98$		0			0
$99$	−63.2797	−	221.885i	−0.0642409	−	0.225255i
$100$		0			0
$101$	−814.290	−	1410.39i	−0.802226	−	1.38950i	−0.918148	−	0.396239i	$-0.870315\pi$
$101$	−814.290	−	1410.39i	−0.802226	−	1.38950i	0.115921	−	0.993258i	$-0.463018\pi$
$102$		0			0
$103$	644.110	+	371.877i	0.616175	+	0.355749i	0.775378	−	0.631497i	$-0.217559\pi$
$103$	644.110	+	371.877i	0.616175	+	0.355749i	−0.159203	+	0.987246i	$0.550893\pi$
$104$		0			0
$105$	−575.827	+	362.207i	−0.535190	+	0.336645i
$106$		0			0
$107$			836.505i			0.755775i	0.925851	+	0.377888i	$0.123349\pi$
$107$			836.505i			0.755775i	−0.925851	+	0.377888i	$0.876651\pi$
$108$		0			0
$109$	−1564.06			−1.37440			−0.687202	−	0.726467i	$-0.741161\pi$
$109$	−1564.06			−1.37440			−0.687202	+	0.726467i	$0.741161\pi$
$110$		0			0
$111$	1224.85	−	955.539i	1.04736	−	0.817079i
$112$		0			0
$113$	−1801.80	−	1040.27i	−1.49999	−	0.866021i	−0.499993	−	0.866029i	$-0.666664\pi$
$113$	−1801.80	−	1040.27i	−1.49999	−	0.866021i	−1.00000		7.94493e-6i	$0.999997\pi$
$114$		0			0
$115$	−1229.28	+	709.725i	−0.996791	+	0.575498i
$116$		0			0
$117$	983.330	−	1015.35i	0.776999	−	0.802297i
$118$		0			0
$119$	−295.875	−	657.988i	−0.227923	−	0.506871i
$120$		0			0
$121$	−628.986	+	1089.44i	−0.472567	+	0.818509i
$122$		0			0
$123$	−318.406	−	2277.44i	−0.233412	−	1.66951i
$124$		0			0
$125$	−1414.00			−1.01178
$126$		0			0
$127$	774.362			0.541051			0.270526	−	0.962713i	$-0.412803\pi$
$127$	774.362			0.541051			0.270526	+	0.962713i	$0.412803\pi$
$128$		0			0
$129$	251.773	+	101.933i	0.171840	+	0.0695715i
$130$		0			0
$131$	402.834	−	697.729i	0.268670	−	0.465350i	−0.699849	−	0.714291i	$-0.746749\pi$
$131$	402.834	−	697.729i	0.268670	−	0.465350i	0.968519	+	0.248941i	$0.0800826\pi$
$132$		0			0
$133$	−1121.58	+	504.339i	−0.731231	+	0.328810i
$134$		0			0
$135$	986.085	+	105.790i	0.628657	+	0.0674439i
$136$		0			0
$137$	1587.40	−	916.484i	0.989930	−	0.571537i	0.0846770	−	0.996408i	$-0.473014\pi$
$137$	1587.40	−	916.484i	0.989930	−	0.571537i	0.905254	+	0.424872i	$0.139681\pi$
$138$		0			0
$139$	−765.487	−	441.954i	−0.467106	−	0.269684i	0.247921	−	0.968780i	$-0.420253\pi$
$139$	−765.487	−	441.954i	−0.467106	−	0.269684i	−0.715028	+	0.699096i	$0.753586\pi$
$140$		0			0
$141$	−1326.26	−	536.952i	−0.792137	−	0.320706i
$142$		0			0
$143$	447.366			0.261613
$144$		0			0
$145$			432.304i			0.247592i
$146$		0			0
$147$	−112.451	+	1778.73i	−0.0630938	+	0.998008i
$148$		0			0
$149$	−1396.08	−	806.025i	−0.767590	−	0.443169i	0.0644239	−	0.997923i	$-0.479479\pi$
$149$	−1396.08	−	806.025i	−0.767590	−	0.443169i	−0.832014	+	0.554754i	$0.812812\pi$
$150$		0			0
$151$	−575.071	−	996.052i	−0.309925	−	0.536805i	0.668421	−	0.743783i	$-0.266970\pi$
$151$	−575.071	−	996.052i	−0.309925	−	0.536805i	−0.978346	+	0.206978i	$0.933637\pi$
$152$		0			0
$153$	−255.913	+	1020.17i	−0.135224	+	0.539057i
$154$		0			0
$155$	822.831	−	475.061i	0.426396	−	0.246180i
$156$		0			0
$157$	1086.53	+	627.309i	0.552322	+	0.318883i	0.750058	−	0.661372i	$-0.230025\pi$
$157$	1086.53	+	627.309i	0.552322	+	0.318883i	−0.197736	+	0.980255i	$0.563359\pi$
$158$		0			0
$159$	436.709	+	559.790i	0.217819	+	0.279209i
$160$		0			0
$161$	−375.051	+	3699.93i	−0.183591	+	1.81115i
$162$		0			0
$163$	1005.42			0.483131			0.241565	−	0.970385i	$-0.422339\pi$
$163$	1005.42			0.483131			0.241565	+	0.970385i	$0.422339\pi$
$164$		0			0
$165$	193.073	+	247.488i	0.0910953	+	0.116769i
$166$		0			0
$167$	1198.49	−	2075.84i	0.555340	−	0.961878i	−0.442536	−	0.896750i	$-0.645921\pi$
$167$	1198.49	−	2075.84i	0.555340	−	0.961878i	0.997877	−	0.0651274i	$-0.0207454\pi$
$168$		0			0
$169$	271.778	+	470.733i	0.123704	+	0.214262i
$170$		0			0
$171$	1738.94	+	436.220i	0.777662	+	0.195080i
$172$		0			0
$173$	15.8922	+	27.5262i	0.00698419	+	0.0120970i	0.869496	−	0.493939i	$-0.164444\pi$
$173$	15.8922	+	27.5262i	0.00698419	+	0.0120970i	−0.862512	+	0.506036i	$0.831110\pi$
$174$		0			0
$175$	−812.611	+	1127.21i	−0.351015	+	0.486907i
$176$		0			0
$177$	275.224	+	1968.57i	0.116876	+	0.835972i
$178$		0			0
$179$		−	1553.05i		−	0.648494i	−0.945972	−	0.324247i	$-0.894889\pi$
$179$		−	1553.05i		−	0.648494i	0.945972	−	0.324247i	$-0.105111\pi$
$180$		0			0
$181$			3516.58i			1.44412i	0.691831	+	0.722059i	$0.256804\pi$
$181$			3516.58i			1.44412i	−0.691831	+	0.722059i	$0.743196\pi$
$182$		0			0
$183$	−589.283	+	1455.52i	−0.238039	+	0.587950i
$184$		0			0
$185$	−1056.69	+	1830.24i	−0.419943	+	0.727362i
$186$		0			0
$187$	−288.293	+	166.446i	−0.112738	+	0.0650895i
$188$		0			0
$189$	1735.63	−	1933.61i	0.667983	−	0.744177i
$190$		0			0
$191$	1971.02	−	1137.97i	0.746692	−	0.431103i	−0.0778056	−	0.996969i	$-0.524791\pi$
$191$	1971.02	−	1137.97i	0.746692	−	0.431103i	0.824497	+	0.565866i	$0.191458\pi$
$192$		0			0
$193$	795.313	−	1377.52i	0.296621	−	0.513763i	−0.678740	−	0.734379i	$-0.737473\pi$
$193$	795.313	−	1377.52i	0.296621	−	0.513763i	0.975361	+	0.220616i	$0.0708068\pi$
$194$		0			0
$195$	−721.608	+	1782.36i	−0.265002	+	0.654550i
$196$		0			0
$197$			1715.67i			0.620490i	0.950657	+	0.310245i	$0.100411\pi$
$197$			1715.67i			0.620490i	−0.950657	+	0.310245i	$0.899589\pi$
$198$		0			0
$199$		−	2534.03i		−	0.902676i	−0.892353	−	0.451338i	$-0.850947\pi$
$199$		−	2534.03i		−	0.902676i	0.892353	−	0.451338i	$-0.149053\pi$
$200$		0			0
$201$	−458.935	−	3282.59i	−0.161049	−	1.15192i
$202$		0			0
$203$	918.760	+	662.342i	0.317657	+	0.229001i
$204$		0			0
$205$	1564.20	+	2709.27i	0.532920	+	0.923044i
$206$		0			0
$207$	3771.78	−	3894.59i	1.26646	−	1.30769i
$208$		0			0
$209$	283.718	+	491.414i	0.0939004	+	0.162640i
$210$		0			0
$211$	2149.79	−	3723.55i	0.701411	−	1.21488i	−0.266560	−	0.963818i	$-0.585887\pi$
$211$	2149.79	−	3723.55i	0.701411	−	1.21488i	0.967971	−	0.251061i	$-0.0807795\pi$
$212$		0			0
$213$	−729.515	−	935.120i	−0.234674	−	0.300814i
$214$		0			0
$215$	−369.523			−0.117215
$216$		0			0
$217$	251.044	−	2476.58i	0.0785345	−	0.774753i
$218$		0			0
$219$	3968.57	+	5087.06i	1.22453	+	1.56964i
$220$		0			0
$221$	−1766.08	−	1019.64i	−0.537553	−	0.310356i
$222$		0			0
$223$	−2529.08	+	1460.16i	−0.759460	+	0.438474i	−0.829102	−	0.559098i	$-0.811148\pi$
$223$	−2529.08	+	1460.16i	−0.759460	+	0.438474i	0.0696418	+	0.997572i	$0.477814\pi$
$224$		0			0
$225$	1948.14	−	555.593i	0.577226	−	0.164620i
$226$		0			0
$227$	−390.119	−	675.705i	−0.114066	−	0.197569i	0.803340	−	0.595521i	$-0.203054\pi$
$227$	−390.119	−	675.705i	−0.114066	−	0.197569i	−0.917406	+	0.397952i	$0.869721\pi$
$228$		0			0
$229$	2843.34	+	1641.61i	0.820495	+	0.473713i	0.850587	−	0.525834i	$-0.176247\pi$
$229$	2843.34	+	1641.61i	0.820495	+	0.473713i	−0.0300919	+	0.999547i	$0.509580\pi$
$230$		0			0
$231$	821.790	−	31.1495i	0.234068	−	0.00887223i
$232$		0			0
$233$			5223.64i			1.46872i	0.678759	+	0.734361i	$0.262518\pi$
$233$			5223.64i			1.46872i	−0.678759	+	0.734361i	$0.737482\pi$
$234$		0			0
$235$	1946.53			0.540330
$236$		0			0
$237$	−969.960	−	392.699i	−0.265847	−	0.107631i
$238$		0			0
$239$	−896.500	−	517.595i	−0.242635	−	0.140085i	0.373752	−	0.927529i	$-0.378071\pi$
$239$	−896.500	−	517.595i	−0.242635	−	0.140085i	−0.616387	+	0.787443i	$0.711404\pi$
$240$		0			0
$241$	4811.53	−	2777.94i	1.28605	−	0.742501i	0.308103	−	0.951353i	$-0.400306\pi$
$241$	4811.53	−	2777.94i	1.28605	−	0.742501i	0.977947	+	0.208852i	$0.0669726\pi$
$242$		0			0
$243$	−3732.78	+	644.382i	−0.985425	+	0.170112i
$244$		0			0
$245$	−766.289	−	2300.37i	−0.199822	−	0.599858i
$246$		0			0
$247$	−1738.05	+	3010.39i	−0.447731	+	0.775493i
$248$		0			0
$249$	−3115.74	−	1261.44i	−0.792980	−	0.321047i
$250$		0			0
$251$	974.838			0.245144			0.122572	−	0.992460i	$-0.460886\pi$
$251$	974.838			0.245144			0.122572	+	0.992460i	$0.460886\pi$
$252$		0			0
$253$	1715.97			0.426412
$254$		0			0
$255$	−198.119	−	1417.07i	−0.0486537	−	0.348002i
$256$		0			0
$257$	−2406.33	+	4167.88i	−0.584057	+	1.01162i	0.410935	+	0.911665i	$0.365202\pi$
$257$	−2406.33	+	4167.88i	−0.584057	+	1.01162i	−0.994992	+	0.0999520i	$0.968131\pi$
$258$		0			0
$259$	2270.77	+	5049.90i	0.544783	+	1.21153i
$260$		0			0
$261$	−452.852	−	1587.89i	−0.107398	−	0.376581i
$262$		0			0
$263$	2132.47	−	1231.18i	0.499976	−	0.288661i	−0.228728	−	0.973490i	$-0.573457\pi$
$263$	2132.47	−	1231.18i	0.499976	−	0.288661i	0.728704	+	0.684829i	$0.240123\pi$
$264$		0			0
$265$	−836.473	−	482.938i	−0.193902	−	0.111950i
$266$		0			0
$267$	−3384.23	+	2640.14i	−0.775698	+	0.605146i
$268$		0			0
$269$	2092.97			0.474389			0.237194	−	0.971462i	$-0.423772\pi$
$269$	2092.97			0.474389			0.237194	+	0.971462i	$0.423772\pi$
$270$		0			0
$271$		−	5006.83i		−	1.12230i	−0.827714	−	0.561150i	$-0.810359\pi$
$271$		−	5006.83i		−	1.12230i	0.827714	−	0.561150i	$-0.189641\pi$
$272$		0			0
$273$	2682.39	+	4264.39i	0.594673	+	0.945395i
$274$		0			0
$275$	555.278	+	320.590i	0.121762	+	0.0702992i
$276$		0			0
$277$	−4158.94	−	7203.49i	−0.902117	−	1.56251i	−0.824742	−	0.565510i	$-0.808680\pi$
$277$	−4158.94	−	7203.49i	−0.902117	−	1.56251i	−0.0773748	−	0.997002i	$-0.524654\pi$
$278$		0			0
$279$	−2524.68	+	2606.88i	−0.541751	+	0.559390i
$280$		0			0
$281$	4024.77	−	2323.70i	0.854440	−	0.493311i	−0.00770671	−	0.999970i	$-0.502453\pi$
$281$	4024.77	−	2323.70i	0.854440	−	0.493311i	0.862146	+	0.506659i	$0.169120\pi$
$282$		0			0
$283$	−3970.15	−	2292.17i	−0.833925	−	0.481467i	0.0212695	−	0.999774i	$-0.493229\pi$
$283$	−3970.15	−	2292.17i	−0.833925	−	0.481467i	−0.855195	+	0.518307i	$0.826563\pi$
$284$		0			0
$285$	−2415.49	+	337.707i	−0.502040	+	0.0701895i
$286$		0			0
$287$	8154.47	+	826.595i	1.67715	+	0.170008i
$288$		0			0
$289$	−3395.53			−0.691132
$290$		0			0
$291$	38.4353	−	94.9343i	0.00774266	−	0.0191242i
$292$		0			0
$293$	−1961.13	+	3396.77i	−0.391025	+	0.677275i	−0.992585	−	0.121552i	$-0.961213\pi$
$293$	−1961.13	+	3396.77i	−0.391025	+	0.677275i	0.601560	+	0.798828i	$0.294546\pi$
$294$		0			0
$295$	−1352.06	−	2341.84i	−0.266848	−	0.462194i
$296$		0			0
$297$	−968.424	−	706.793i	−0.189204	−	0.138089i
$298$		0			0
$299$	5256.01	+	9103.67i	1.01660	+	1.76080i
$300$		0			0
$301$	−566.154	+	785.334i	−0.108414	+	0.150385i
$302$		0			0
$303$	−7843.88	−	3175.68i	−1.48719	−	0.602107i
$304$		0			0
$305$		−	2136.24i		−	0.401051i
$306$		0			0
$307$		−	8034.65i		−	1.49369i	−0.665000	−	0.746843i	$-0.731569\pi$
$307$		−	8034.65i		−	1.49369i	0.665000	−	0.746843i	$-0.268431\pi$
$308$		0			0
$309$	3827.43	−	535.109i	0.704644	−	0.0985154i
$310$		0			0
$311$	2215.47	−	3837.30i	0.403947	−	0.699657i	−0.590251	−	0.807220i	$-0.700971\pi$
$311$	2215.47	−	3837.30i	0.403947	−	0.699657i	0.994198	+	0.107563i	$0.0343047\pi$
$312$		0			0
$313$	5126.22	−	2959.63i	0.925723	−	0.534467i	0.0402668	−	0.999189i	$-0.487179\pi$
$313$	5126.22	−	2959.63i	0.925723	−	0.534467i	0.885456	+	0.464722i	$0.153846\pi$
$314$		0			0
$315$	−1201.46	+	3324.35i	−0.214903	+	0.594622i
$316$		0			0
$317$	458.040	−	264.450i	0.0811549	−	0.0468548i	−0.458873	−	0.888502i	$-0.651747\pi$
$317$	458.040	−	264.450i	0.0811549	−	0.0468548i	0.540028	+	0.841647i	$0.318414\pi$
$318$		0			0
$319$	261.306	−	452.595i	0.0458630	−	0.0794371i
$320$		0			0
$321$	2673.58	+	3427.09i	0.464874	+	0.595893i
$322$		0			0
$323$		−	2586.62i		−	0.445583i
$324$		0			0
$325$			3927.85i			0.670394i
$326$		0			0
$327$	−6407.84	+	4998.95i	−1.08365	+	0.845390i
$328$		0			0
$329$	2982.32	−	4136.89i	0.499759	−	0.693235i
$330$		0			0
$331$	1824.88	+	3160.78i	0.303035	+	0.524871i	0.976822	−	0.214054i	$-0.0686669\pi$
$331$	1824.88	+	3160.78i	0.303035	+	0.524871i	−0.673787	+	0.738925i	$0.735334\pi$
$332$		0			0
$333$	1964.07	−	7829.53i	0.323214	−	1.28846i
$334$		0			0
$335$	2254.56	+	3905.02i	0.367701	+	0.636878i
$336$		0			0
$337$	−3284.70	+	5689.26i	−0.530946	+	0.919625i	0.468402	+	0.883516i	$0.344830\pi$
$337$	−3284.70	+	5689.26i	−0.530946	+	0.919625i	−0.999348	+	0.0361099i	$0.988503\pi$
$338$		0			0
$339$	−10706.7	+	1496.89i	−1.71536	+	0.239822i
$340$		0			0
$341$	−1148.60			−0.182405
$342$		0			0
$343$	−6062.94	−	1895.88i	−0.954426	−	0.298448i
$344$		0			0
$345$	−2767.89	+	6836.63i	−0.431937	+	1.06687i
$346$		0			0
$347$	−10270.0	−	5929.38i	−1.58882	−	0.917307i	−0.993501	−	0.113820i	$-0.963691\pi$
$347$	−10270.0	−	5929.38i	−1.58882	−	0.917307i	−0.595321	−	0.803488i	$-0.702975\pi$
$348$		0			0
$349$	30.7558	−	17.7568i	0.00471724	−	0.00272350i	−0.497640	−	0.867384i	$-0.665800\pi$
$349$	30.7558	−	17.7568i	0.00471724	−	0.00272350i	0.502357	+	0.864660i	$0.332466\pi$
$350$		0			0
$351$	783.446	−	7302.64i	0.119137	−	1.11050i
$352$		0			0
$353$	4968.07	+	8604.94i	0.749075	+	1.29744i	0.948266	+	0.317475i	$0.102835\pi$
$353$	4968.07	+	8604.94i	0.749075	+	1.29744i	−0.199191	+	0.979961i	$0.563832\pi$
$354$		0			0
$355$	1397.31	+	806.740i	0.208906	+	0.120612i
$356$		0			0
$357$	−3315.19	−	1750.07i	−0.491481	−	0.259450i
$358$		0			0
$359$			10087.1i			1.48295i	0.670983	+	0.741473i	$0.265872\pi$
$359$			10087.1i			1.48295i	−0.670983	+	0.741473i	$0.734128\pi$
$360$		0			0
$361$	2449.94			0.357186
$362$		0			0
$363$	905.073	+	6473.65i	0.130865	+	0.936030i
$364$		0			0
$365$	−7601.41	−	4388.68i	−1.09007	−	0.629353i
$366$		0			0
$367$	8473.74	−	4892.32i	1.20525	−	0.695850i	0.243530	−	0.969893i	$-0.421695\pi$
$367$	8473.74	−	4892.32i	1.20525	−	0.695850i	0.961717	+	0.274044i	$0.0883612\pi$
$368$		0			0
$369$	−8583.48	−	8312.82i	−1.21094	−	1.17276i
$370$		0			0
$371$	−2307.95	+	1037.81i	−0.322972	+	0.145230i
$372$		0			0
$373$	3884.31	−	6727.82i	0.539201	−	0.933923i	−0.459747	−	0.888050i	$-0.652060\pi$
$373$	3884.31	−	6727.82i	0.539201	−	0.933923i	0.998947	−	0.0458729i	$-0.0146069\pi$
$374$		0			0
$375$	−5793.04	+	4519.33i	−0.797737	+	0.622339i
$376$		0			0
$377$	3201.51			0.437364
$378$		0			0
$379$	−10683.1			−1.44789			−0.723947	−	0.689856i	$-0.757674\pi$
$379$	−10683.1			−1.44789			−0.723947	+	0.689856i	$0.757674\pi$
$380$		0			0
$381$	3172.50	−	2474.96i	0.426593	−	0.332798i
$382$		0			0
$383$	−6456.89	+	11183.7i	−0.861440	+	1.49206i	0.00909866	+	0.999959i	$0.497104\pi$
$383$	−6456.89	+	11183.7i	−0.861440	+	1.49206i	−0.870539	+	0.492100i	$0.836230\pi$
$384$		0			0
$385$	−1020.37	+	458.825i	−0.135072	+	0.0607373i
$386$		0			0
$387$	1357.29	−	387.087i	0.178281	−	0.0508443i
$388$		0			0
$389$	9760.56	−	5635.26i	1.27218	−	0.734496i	0.296786	−	0.954944i	$-0.404085\pi$
$389$	9760.56	−	5635.26i	1.27218	−	0.734496i	0.975399	+	0.220448i	$0.0707518\pi$
$390$		0			0
$391$	−6774.18	−	3911.07i	−0.876176	−	0.505861i
$392$		0			0
$393$	−579.654	−	4146.05i	−0.0744012	−	0.532164i
$394$		0			0
$395$	1423.59			0.181339
$396$		0			0
$397$		−	4908.58i		−	0.620540i	−0.950648	−	0.310270i	$-0.899581\pi$
$397$		−	4908.58i		−	0.620540i	0.950648	−	0.310270i	$-0.100419\pi$
$398$		0			0
$399$	−2983.11	+	5650.97i	−0.374291	+	0.709028i
$400$		0			0
$401$	−4193.64	−	2421.20i	−0.522246	−	0.301519i	0.215607	−	0.976480i	$-0.430827\pi$
$401$	−4193.64	−	2421.20i	−0.522246	−	0.301519i	−0.737853	+	0.674961i	$0.764160\pi$
$402$		0			0
$403$	−3518.16	−	6093.63i	−0.434868	−	0.753214i
$404$		0			0
$405$	4378.03	−	2718.25i	0.537151	−	0.333508i
$406$		0			0
$407$	2212.58	−	1277.43i	0.269468	−	0.155577i
$408$		0			0
$409$	−421.586	−	243.403i	−0.0509684	−	0.0294266i	0.474299	−	0.880364i	$-0.342701\pi$
$409$	−421.586	−	243.403i	−0.0509684	−	0.0294266i	−0.525268	+	0.850937i	$0.676035\pi$
$410$		0			0
$411$	3574.24	−	8828.29i	0.428964	−	1.05953i
$412$		0			0
$413$	−7048.56	−	714.492i	−0.839799	−	0.0851280i
$414$		0			0
$415$	4572.92			0.540905
$416$		0			0
$417$	−4548.68	+	635.946i	−0.534173	+	0.0746820i
$418$		0			0
$419$	6580.88	−	11398.4i	0.767296	−	1.32900i	−0.171728	−	0.985144i	$-0.554935\pi$
$419$	6580.88	−	11398.4i	0.767296	−	1.32900i	0.939024	−	0.343851i	$-0.111732\pi$
$420$		0			0
$421$	−848.070	−	1468.90i	−0.0981767	−	0.170047i	0.812753	−	0.582608i	$-0.197968\pi$
$421$	−848.070	−	1468.90i	−0.0981767	−	0.170047i	−0.910930	+	0.412561i	$0.864634\pi$
$422$		0			0
$423$	−7149.75	+	2039.05i	−0.821827	+	0.234378i
$424$		0			0
$425$	−1461.39	−	2531.20i	−0.166795	−	0.288897i
$426$		0			0
$427$	−4540.07	−	3272.97i	−0.514542	−	0.370937i
$428$		0			0
$429$	1832.82	−	1429.84i	0.206269	−	0.160917i
$430$		0			0
$431$			3662.97i			0.409372i	0.978828	+	0.204686i	$0.0656173\pi$
$431$			3662.97i			0.409372i	−0.978828	+	0.204686i	$0.934383\pi$
$432$		0			0
$433$			5695.06i			0.632071i	0.948747	+	0.316036i	$0.102352\pi$
$433$			5695.06i			0.632071i	−0.948747	+	0.316036i	$0.897648\pi$
$434$		0			0
$435$	1381.70	+	1771.11i	0.152293	+	0.195215i
$436$		0			0
$437$	−6666.68	+	11547.0i	−0.729773	+	1.26400i
$438$		0			0
$439$	12705.5	−	7335.54i	1.38132	−	0.797508i	0.389008	−	0.921234i	$-0.372818\pi$
$439$	12705.5	−	7335.54i	1.38132	−	0.797508i	0.992316	+	0.123726i	$0.0394845\pi$
$440$		0			0
$441$	5224.35	+	7646.72i	0.564124	+	0.825690i
$442$		0			0
$443$	3537.20	−	2042.20i	0.379362	−	0.219025i	−0.298179	−	0.954510i	$-0.596379\pi$
$443$	3537.20	−	2042.20i	0.379362	−	0.219025i	0.677541	+	0.735485i	$0.263046\pi$
$444$		0			0
$445$	2919.62	−	5056.93i	0.311018	−	0.538700i
$446$		0			0
$447$	−8295.77	+	1159.82i	−0.877800	+	0.122724i
$448$		0			0
$449$			17057.8i			1.79289i	0.443160	+	0.896443i	$0.353857\pi$
$449$			17057.8i			1.79289i	−0.443160	+	0.896443i	$0.646143\pi$
$450$		0			0
$451$		−	3781.92i		−	0.394864i
$452$		0			0
$453$	−5539.53	−	2242.74i	−0.574547	−	0.232612i
$454$		0			0
$455$	−5559.56	−	4007.93i	−0.572826	−	0.412955i
$456$		0			0
$457$	−1850.19	−	3204.63i	−0.189384	−	0.328022i	0.755661	−	0.654963i	$-0.227316\pi$
$457$	−1850.19	−	3204.63i	−0.189384	−	0.328022i	−0.945045	+	0.326940i	$0.893982\pi$
$458$		0			0
$459$	2212.13	+	4997.48i	0.224953	+	0.508196i
$460$		0			0
$461$	−6736.65	−	11668.2i	−0.680601	−	1.17884i	−0.974798	−	0.223091i	$-0.928385\pi$
$461$	−6736.65	−	11668.2i	−0.680601	−	1.17884i	0.294197	−	0.955745i	$-0.404948\pi$
$462$		0			0
$463$	−1550.96	+	2686.34i	−0.155678	+	0.269643i	−0.933306	−	0.359082i	$-0.883090\pi$
$463$	−1550.96	+	2686.34i	−0.155678	+	0.269643i	0.777627	+	0.628725i	$0.216423\pi$
$464$		0			0
$465$	1852.71	−	4576.16i	0.184769	−	0.456375i
$466$		0			0
$467$	12591.3			1.24766			0.623828	−	0.781561i	$-0.285576\pi$
$467$	12591.3			1.24766			0.623828	+	0.781561i	$0.285576\pi$
$468$		0			0
$469$	11753.5	+	1191.41i	1.15720	+	0.117302i
$470$		0			0
$471$	6456.39	−	902.660i	0.631624	−	0.0883065i
$472$		0			0
$473$	386.867	+	223.358i	0.0376071	+	0.0217125i
$474$		0			0
$475$	−4314.59	+	2491.03i	−0.416773	+	0.240624i
$476$		0			0
$477$	3578.32	+	897.635i	0.343480	+	0.0861633i
$478$		0			0
$479$	2640.55	+	4573.56i	0.251878	+	0.436266i	0.964043	−	0.265747i	$-0.0856184\pi$
$479$	2640.55	+	4573.56i	0.251878	+	0.436266i	−0.712165	+	0.702012i	$0.752285\pi$
$480$		0			0
$481$	13554.2	+	7825.52i	1.28486	+	0.741815i
$482$		0			0
$483$	10288.9	+	16357.0i	0.969278	+	1.54093i
$484$		0			0
$485$			139.333i			0.0130450i
$486$		0			0
$487$	945.042			0.0879341			0.0439671	−	0.999033i	$-0.486000\pi$
$487$	945.042			0.0879341			0.0439671	+	0.999033i	$0.486000\pi$
$488$		0			0
$489$	4119.11	−	3213.44i	0.380926	−	0.297171i
$490$		0			0
$491$	−1326.45	−	765.828i	−0.121919	−	0.0703897i	0.437801	−	0.899072i	$-0.355758\pi$
$491$	−1326.45	−	765.828i	−0.121919	−	0.0703897i	−0.559719	+	0.828682i	$0.689091\pi$
$492$		0			0
$493$	−2063.12	+	1191.15i	−0.188476	+	0.108816i
$494$		0			0
$495$	1582.01	+	396.853i	0.143649	+	0.0360348i
$496$		0			0
$497$	3855.39	−	1733.64i	0.347964	−	0.156468i
$498$		0			0
$499$	−6853.72	+	11871.0i	−0.614859	+	1.06497i	0.375550	+	0.926802i	$0.377454\pi$
$499$	−6853.72	+	11871.0i	−0.614859	+	1.06497i	−0.990409	+	0.138165i	$0.955879\pi$
$500$		0			0
$501$	−1724.55	−	12335.1i	−0.153787	−	1.09998i
$502$		0			0
$503$	17261.6			1.53013			0.765065	−	0.643953i	$-0.222707\pi$
$503$	17261.6			1.53013			0.765065	+	0.643953i	$0.222707\pi$
$504$		0			0
$505$	11512.3			1.01444
$506$		0			0
$507$	2617.97	+	1059.92i	0.229326	+	0.0928453i
$508$		0			0
$509$	−6542.31	+	11331.6i	−0.569711	+	0.986768i	0.426884	+	0.904307i	$0.359611\pi$
$509$	−6542.31	+	11331.6i	−0.569711	+	0.986768i	−0.996594	+	0.0824613i	$0.973722\pi$
$510$		0			0
$511$	−20973.4	+	9431.03i	−1.81567	+	0.816446i
$512$		0			0
$513$	8518.52	−	3770.73i	0.733142	−	0.324526i
$514$		0			0
$515$	−4553.17	+	2628.77i	−0.389586	+	0.224927i
$516$		0			0
$517$	−2037.89	−	1176.58i	−0.173359	−	0.100089i
$518$		0			0
$519$	153.087	+	61.9789i	0.0129475	+	0.00524195i
$520$		0			0
$521$	−12720.6			−1.06967			−0.534835	−	0.844956i	$-0.679626\pi$
$521$	−12720.6			−1.06967			−0.534835	+	0.844956i	$0.679626\pi$
$522$		0			0
$523$		−	1352.20i		−	0.113055i	−0.998401	−	0.0565274i	$-0.981997\pi$
$523$		−	1352.20i		−	0.113055i	0.998401	−	0.0565274i	$-0.0180028\pi$
$524$		0			0
$525$	273.491	+	7215.28i	0.0227355	+	0.599811i
$526$		0			0
$527$	4534.36	+	2617.91i	0.374801	+	0.216391i
$528$		0			0
$529$	14077.1	+	24382.2i	1.15699	+	2.00396i
$530$		0			0
$531$	7419.38	+	7185.43i	0.606354	+	0.587234i
$532$		0			0
$533$	20064.0	−	11584.0i	1.63053	−	0.941385i
$534$		0			0
$535$	−5120.98	−	2956.60i	−0.413830	−	0.238925i
$536$		0			0
$537$	−4963.75	−	6362.72i	−0.398886	−	0.511307i
$538$		0			0
$539$	−588.200	+	2871.52i	−0.0470048	+	0.229472i
$540$		0			0
$541$	−8023.06			−0.637594			−0.318797	−	0.947823i	$-0.603279\pi$
$541$	−8023.06			−0.637594			−0.318797	+	0.947823i	$0.603279\pi$
$542$		0			0
$543$	11239.5	+	14407.1i	0.888271	+	1.13862i
$544$		0			0
$545$	5528.13	−	9574.99i	0.434493	−	0.752565i
$546$		0			0
$547$	966.417	+	1673.88i	0.0755411	+	0.130841i	0.901321	−	0.433151i	$-0.142598\pi$
$547$	966.417	+	1673.88i	0.0755411	+	0.130841i	−0.825780	+	0.563992i	$0.809265\pi$
$548$		0			0
$549$	2237.78	+	7846.56i	0.173964	+	0.609988i
$550$		0			0
$551$	2030.39	+	3516.73i	0.156982	+	0.271902i
$552$		0			0
$553$	2181.12	−	3025.51i	0.167722	−	0.232654i
$554$		0			0
$555$	1520.51	+	10875.7i	0.116292	+	0.831796i
$556$		0			0
$557$		−	3185.91i		−	0.242354i	−0.992631	−	0.121177i	$-0.961333\pi$
$557$		−	3185.91i		−	0.242354i	0.992631	−	0.121177i	$-0.0386669\pi$
$558$		0			0
$559$			2736.57i			0.207057i
$560$		0			0
$561$	−649.130	+	1603.34i	−0.0488525	+	0.120665i
$562$		0			0
$563$	5544.17	−	9602.79i	0.415025	−	0.718844i	−0.580406	−	0.814327i	$-0.697106\pi$
$563$	5544.17	−	9602.79i	0.415025	−	0.718844i	0.995431	+	0.0954828i	$0.0304395\pi$
$564$		0			0
$565$	12736.8	−	7353.60i	0.948392	−	0.547555i
$566$		0			0
$567$	930.679	−	13469.2i	0.0689327	−	0.997621i
$568$		0			0
$569$	4166.78	−	2405.69i	0.306995	−	0.177244i	−0.338586	−	0.940936i	$-0.609949\pi$
$569$	4166.78	−	2405.69i	0.306995	−	0.177244i	0.645581	+	0.763692i	$0.276615\pi$
$570$		0			0
$571$	1711.30	−	2964.07i	0.125422	−	0.217237i	−0.796476	−	0.604670i	$-0.793305\pi$
$571$	1711.30	−	2964.07i	0.125422	−	0.217237i	0.921898	+	0.387433i	$0.126638\pi$
$572$		0			0
$573$	4438.02	−	10961.8i	0.323562	−	0.799191i
$574$		0			0
$575$			15066.2i			1.09270i
$576$		0			0
$577$			15586.3i			1.12455i	0.826950	+	0.562275i	$0.190074\pi$
$577$			15586.3i			1.12455i	−0.826950	+	0.562275i	$0.809926\pi$
$578$		0			0
$579$	−1144.41	−	8185.52i	−0.0821415	−	0.587528i
$580$		0			0
$581$	7006.26	−	9718.66i	0.500290	−	0.693973i
$582$		0			0
$583$	583.823	+	1011.21i	0.0414742	+	0.0718354i
$584$		0			0
$585$	2740.28	+	9608.53i	0.193669	+	0.679083i
$586$		0			0
$587$	−12308.5	−	21319.0i	−0.865465	−	1.49903i	−0.866584	−	0.499031i	$-0.833690\pi$
$587$	−12308.5	−	21319.0i	−0.865465	−	1.49903i	0.00111897	−	0.999999i	$-0.499644\pi$
$588$		0			0
$589$	4462.41	−	7729.12i	0.312174	−	0.540701i
$590$		0			0
$591$	5483.51	+	7028.97i	0.381661	+	0.489227i
$592$		0			0
$593$	−25080.0			−1.73678			−0.868392	−	0.495878i	$-0.834846\pi$
$593$	−25080.0			−1.73678			−0.868392	+	0.495878i	$0.834846\pi$
$594$		0			0
$595$	5073.88	+	514.325i	0.349595	+	0.0354374i
$596$		0			0
$597$	−8099.09	−	10381.7i	−0.555232	−	0.711718i
$598$		0			0
$599$	11208.0	+	6470.92i	0.764516	+	0.441394i	0.830915	−	0.556400i	$-0.187818\pi$
$599$	11208.0	+	6470.92i	0.764516	+	0.441394i	−0.0663988	+	0.997793i	$0.521151\pi$
$600$		0			0
$601$	−11568.5	+	6679.10i	−0.785176	+	0.453321i	−0.838261	−	0.545269i	$-0.816428\pi$
$601$	−11568.5	+	6679.10i	−0.785176	+	0.453321i	0.0530857	+	0.998590i	$0.483094\pi$
$602$		0			0
$603$	−12371.8	−	11981.7i	−0.835521	−	0.809175i
$604$		0			0
$605$	−4446.26	−	7701.15i	−0.298787	−	0.517514i
$606$		0			0
$607$	9551.96	+	5514.83i	0.638718	+	0.368764i	0.784121	−	0.620608i	$-0.213114\pi$
$607$	9551.96	+	5514.83i	0.638718	+	0.368764i	−0.145402	+	0.989373i	$0.546448\pi$
$608$		0			0
$609$	5881.02	−	222.917i	0.391315	−	0.0148326i
$610$		0			0
$611$		−	14415.4i		−	0.954475i
$612$		0			0
$613$	−9716.71			−0.640219			−0.320109	−	0.947381i	$-0.603720\pi$
$613$	−9716.71			−0.640219			−0.320109	+	0.947381i	$0.603720\pi$
$614$		0			0
$615$	15067.6	+	6100.29i	0.987942	+	0.399980i
$616$		0			0
$617$	19367.5	+	11181.9i	1.26371	+	0.729602i	0.973790	−	0.227449i	$-0.0730386\pi$
$617$	19367.5	+	11181.9i	1.26371	+	0.729602i	0.289918	+	0.957051i	$0.406372\pi$
$618$		0			0
$619$	−5030.74	+	2904.50i	−0.326660	+	0.188597i	−0.654357	−	0.756186i	$-0.727061\pi$
$619$	−5030.74	+	2904.50i	−0.326660	+	0.188597i	0.327697	+	0.944783i	$0.393727\pi$
$620$		0			0
$621$	3005.08	−	28010.9i	0.194186	−	1.81005i
$622$		0			0
$623$	−6274.10	−	13952.8i	−0.403478	−	0.897282i
$624$		0			0
$625$	308.348	−	534.075i	0.0197343	−	0.0341808i
$626$		0			0
$627$	2732.99	+	1106.48i	0.174075	+	0.0704764i
$628$		0			0
$629$	−11646.2			−0.738257
$630$		0			0
$631$	−11462.0			−0.723128			−0.361564	−	0.932347i	$-0.617757\pi$
$631$	−11462.0			−0.723128			−0.361564	+	0.932347i	$0.617757\pi$
$632$		0			0
$633$	−3093.42	−	22126.1i	−0.194238	−	1.38931i
$634$		0			0
$635$	−2736.96	+	4740.55i	−0.171044	+	0.296257i
$636$		0			0
$637$	−17035.8	+	5674.90i	−1.05963	+	0.352979i
$638$		0			0
$639$	−5977.53	−	1499.49i	−0.370058	−	0.0928306i
$640$		0			0
$641$	−22256.6	+	12849.8i	−1.37142	+	0.791791i	−0.991107	−	0.133066i	$-0.957518\pi$
$641$	−22256.6	+	12849.8i	−1.37142	+	0.791791i	−0.380315	+	0.924857i	$0.624184\pi$
$642$		0			0
$643$	−14555.9	−	8403.85i	−0.892735	−	0.515421i	−0.0178986	−	0.999840i	$-0.505698\pi$
$643$	−14555.9	−	8403.85i	−0.892735	−	0.515421i	−0.874836	+	0.484419i	$0.839031\pi$
$644$		0			0
$645$	−1513.91	+	1181.04i	−0.0924186	+	0.0720985i
$646$		0			0
$647$	−14607.3			−0.887595			−0.443798	−	0.896127i	$-0.646369\pi$
$647$	−14607.3			−0.887595			−0.443798	+	0.896127i	$0.646369\pi$
$648$		0			0
$649$			3269.01i			0.197720i
$650$		0			0
$651$	−6886.98	−	10948.7i	−0.414627	−	0.659163i
$652$		0			0
$653$	−23324.4	−	13466.4i	−1.39779	−	0.807013i	−0.403627	−	0.914924i	$-0.632251\pi$
$653$	−23324.4	−	13466.4i	−1.39779	−	0.807013i	−0.994161	+	0.107911i	$0.965584\pi$
$654$		0			0
$655$	2847.61	+	4932.20i	0.169870	+	0.294224i
$656$		0			0
$657$	32517.8	+	8157.22i	1.93096	+	0.484389i
$658$		0			0
$659$	−21546.5	+	12439.9i	−1.27364	+	0.735339i	−0.975672	−	0.219235i	$-0.929644\pi$
$659$	−21546.5	+	12439.9i	−1.27364	+	0.735339i	−0.297973	+	0.954574i	$0.596310\pi$
$660$		0			0
$661$	24869.6	+	14358.5i	1.46341	+	0.844902i	0.999167	−	0.0408035i	$-0.0129918\pi$
$661$	24869.6	+	14358.5i	1.46341	+	0.844902i	0.464247	+	0.885706i	$0.346325\pi$
$662$		0			0
$663$	−10494.4	+	1467.21i	−0.614734	+	0.0859451i
$664$		0			0
$665$	876.701	−	8648.77i	0.0511233	−	0.504338i
$666$		0			0
$667$	12280.1			0.712874
$668$		0			0
$669$	−5694.56	+	14065.4i	−0.329095	+	0.812857i
$670$		0			0
$671$	−1291.25	+	2236.51i	−0.0742892	+	0.128673i
$672$		0			0
$673$	−487.441	−	844.272i	−0.0279190	−	0.0483570i	0.851728	−	0.523984i	$-0.175555\pi$
$673$	−487.441	−	844.272i	−0.0279190	−	0.0483570i	−0.879647	+	0.475627i	$0.842221\pi$
$674$		0			0
$675$	6205.62	−	8502.73i	0.353858	−	0.484845i
$676$		0			0
$677$	10639.0	+	18427.4i	0.603976	+	1.04612i	0.992212	+	0.124557i	$0.0397511\pi$
$677$	10639.0	+	18427.4i	0.603976	+	1.04612i	−0.388236	+	0.921560i	$0.626916\pi$
$678$		0			0
$679$	296.121	+	213.476i	0.0167365	+	0.0120655i
$680$		0			0
$681$	−3757.93	−	1521.44i	−0.211460	−	0.0856120i
$682$		0			0
$683$		−	6554.78i		−	0.367221i	−0.982999	−	0.183610i	$-0.941222\pi$
$683$		−	6554.78i		−	0.367221i	0.982999	−	0.183610i	$-0.0587785\pi$
$684$		0			0
$685$			12957.1i			0.722725i
$686$		0			0
$687$	16895.7	−	2362.17i	0.938301	−	0.131183i
$688$		0			0
$689$	−3576.49	+	6194.66i	−0.197755	+	0.342522i
$690$		0			0
$691$	−7567.47	+	4369.08i	−0.416614	+	0.240532i	−0.693627	−	0.720334i	$-0.743989\pi$
$691$	−7567.47	+	4369.08i	−0.416614	+	0.240532i	0.277014	+	0.960866i	$0.410655\pi$
$692$		0			0
$693$	3267.25	−	2754.16i	0.179095	−	0.150970i
$694$		0			0
$695$	5411.18	−	3124.15i	0.295335	−	0.170512i
$696$		0			0
$697$	−8619.82	+	14930.0i	−0.468435	+	0.811353i
$698$		0			0
$699$	16695.4	+	21400.8i	0.903404	+	1.15802i
$700$		0			0
$701$		−	9016.22i		−	0.485789i	−0.970053	−	0.242894i	$-0.921903\pi$
$701$		−	9016.22i		−	0.485789i	0.970053	−	0.242894i	$-0.0780969\pi$
$702$		0			0
$703$			19851.7i			1.06504i
$704$		0			0
$705$	7974.78	−	6221.36i	0.426025	−	0.332355i
$706$		0			0
$707$	17638.3	−	24466.7i	0.938268	−	1.30151i
$708$		0			0
$709$	−14131.7	−	24476.8i	−0.748557	−	1.29654i	−0.948515	−	0.316734i	$-0.897414\pi$
$709$	−14131.7	−	24476.8i	−0.748557	−	1.29654i	0.199958	−	0.979804i	$-0.435919\pi$
$710$		0			0
$711$	−5228.97	+	1491.26i	−0.275811	+	0.0786591i
$712$		0			0
$713$	−13494.7	−	23373.5i	−0.708807	−	1.22769i
$714$		0			0
$715$	−1581.20	+	2738.72i	−0.0827042	+	0.143248i
$716$		0			0
$717$	−5327.19	+	744.788i	−0.277472	+	0.0387930i
$718$		0			0
$719$	−23753.1			−1.23205			−0.616023	−	0.787728i	$-0.711257\pi$
$719$	−23753.1			−1.23205			−0.616023	+	0.787728i	$0.711257\pi$
$720$		0			0
$721$	−1389.16	+	13704.3i	−0.0717548	+	0.707870i
$722$		0			0
$723$	10833.8	−	26759.3i	0.557280	−	1.37647i
$724$		0			0
$725$	3973.76	+	2294.25i	0.203561	+	0.117526i
$726$		0			0
$727$	−23109.1	+	13342.1i	−1.17891	+	0.680645i	−0.955763	−	0.294139i	$-0.904967\pi$
$727$	−23109.1	+	13342.1i	−1.17891	+	0.680645i	−0.223150	+	0.974784i	$0.571634\pi$
$728$		0			0
$729$	−13233.4	+	14570.4i	−0.672326	+	0.740255i
$730$		0			0
$731$	−1018.16	−	1763.51i	−0.0515159	−	0.0892281i
$732$		0			0
$733$	29171.7	+	16842.3i	1.46996	+	0.848684i	0.999432	−	0.0337000i	$-0.0107291\pi$
$733$	29171.7	+	16842.3i	1.46996	+	0.848684i	0.470531	+	0.882383i	$0.344062\pi$
$734$		0			0
$735$	−10491.7	−	6975.27i	−0.526520	−	0.350050i
$736$		0			0
$737$		−	5451.08i		−	0.272446i
$738$		0			0
$739$	1602.94			0.0797905			0.0398952	−	0.999204i	$-0.487298\pi$
$739$	1602.94			0.0797905			0.0398952	+	0.999204i	$0.487298\pi$
$740$		0			0
$741$	2500.95	+	17888.4i	0.123987	+	0.886836i
$742$		0			0
$743$	−33905.7	−	19575.5i	−1.67413	−	0.966560i	−0.965285	−	0.261197i	$-0.915883\pi$
$743$	−33905.7	−	19575.5i	−1.67413	−	0.966560i	−0.708846	−	0.705363i	$-0.750784\pi$
$744$		0			0
$745$	9868.76	−	5697.73i	0.485320	−	0.280200i
$746$		0			0
$747$	−16796.7	+	4790.28i	−0.822702	+	0.234628i
$748$		0			0
$749$	−14129.5	+	6353.57i	−0.689294	+	0.309952i
$750$		0			0
$751$	10417.9	−	18044.4i	0.506199	−	0.876762i	−0.493775	−	0.869590i	$-0.664383\pi$
$751$	10417.9	−	18044.4i	0.506199	−	0.876762i	0.999974	−	0.00717280i	$-0.00228319\pi$
$752$		0			0
$753$	3993.83	−	3115.71i	0.193285	−	0.150787i
$754$		0			0
$755$	8130.28			0.391909
$756$		0			0
$757$	1105.00			0.0530538			0.0265269	−	0.999648i	$-0.491555\pi$
$757$	1105.00			0.0530538			0.0265269	+	0.999648i	$0.491555\pi$
$758$		0			0
$759$	7030.20	−	5484.47i	0.336206	−	0.262284i
$760$		0			0
$761$	−13772.2	+	23854.2i	−0.656036	+	1.13629i	0.325597	+	0.945508i	$0.394435\pi$
$761$	−13772.2	+	23854.2i	−0.656036	+	1.13629i	−0.981633	+	0.190779i	$0.938899\pi$
$762$		0			0
$763$	−11879.6	−	26418.8i	−0.563659	−	1.25350i
$764$		0			0
$765$	−5340.82	−	5172.41i	−0.252415	−	0.244456i
$766$		0			0
$767$	−17342.9	+	10013.0i	−0.816451	+	0.471378i
$768$		0			0
$769$	−10418.2	−	6014.95i	−0.488543	−	0.282060i	0.235427	−	0.971892i	$-0.424351\pi$
$769$	−10418.2	−	6014.95i	−0.488543	−	0.282060i	−0.723970	+	0.689832i	$0.757685\pi$
$770$		0			0
$771$	3462.56	+	24766.4i	0.161740	+	1.15686i
$772$		0			0
$773$	20325.9			0.945758			0.472879	−	0.881127i	$-0.343215\pi$
$773$	20325.9			0.945758			0.472879	+	0.881127i	$0.343215\pi$
$774$		0			0
$775$		−	10084.7i		−	0.467422i
$776$		0			0
$777$	25443.3	+	13431.3i	1.17474	+	0.620138i
$778$		0			0
$779$	25449.1	+	14693.0i	1.17049	+	0.675780i
$780$		0			0
$781$	−975.266	−	1689.21i	−0.0446834	−	0.0773940i
$782$		0			0
$783$	−6930.39	−	5058.06i	−0.316311	−	0.230856i
$784$		0			0
$785$	−7680.61	+	4434.40i	−0.349214	+	0.201619i
$786$		0			0
$787$	−22900.0	−	13221.3i	−1.03722	−	0.598842i	−0.118178	−	0.992992i	$-0.537705\pi$
$787$	−22900.0	−	13221.3i	−1.03722	−	0.598842i	−0.919046	+	0.394151i	$0.871039\pi$
$788$		0			0
$789$	4801.54	−	11859.7i	0.216653	−	0.535129i
$790$		0			0
$791$	3885.98	−	38335.7i	0.174677	−	1.72321i
$792$		0			0
$793$	−15820.3			−0.708443
$794$		0			0
$795$	−4970.49	+	694.919i	−0.221742	+	0.0310015i
$796$		0			0
$797$	13176.4	−	22822.2i	0.585612	−	1.01431i	−0.409187	−	0.912451i	$-0.634187\pi$
$797$	13176.4	−	22822.2i	0.585612	−	1.01431i	0.994799	−	0.101859i	$-0.0324792\pi$
$798$		0			0
$799$	5363.36	+	9289.61i	0.237474	+	0.411318i
$800$		0			0
$801$	−5426.69	+	21632.9i	−0.239379	+	0.954257i
$802$		0			0
$803$	5305.46	+	9189.33i	0.233158	+	0.403841i
$804$		0			0
$805$	−21324.9	−	15373.3i	−0.933670	−	0.673090i
$806$		0			0
$807$	8574.72	−	6689.40i	0.374033	−	0.291794i
$808$		0			0
$809$			36209.0i			1.57360i	0.617211	+	0.786798i	$0.288263\pi$
$809$			36209.0i			1.57360i	−0.617211	+	0.786798i	$0.711737\pi$
$810$		0			0
$811$			12130.9i			0.525245i	0.964899	+	0.262622i	$0.0845874\pi$
$811$			12130.9i			0.525245i	−0.964899	+	0.262622i	$0.915413\pi$
$812$		0			0
$813$	−16002.5	−	20512.6i	−0.690322	−	0.884880i
$814$		0			0
$815$	−3553.61	+	6155.03i	−0.152733	+	0.264542i
$816$		0			0
$817$	−3006.02	+	1735.53i	−0.128724	+	0.0743186i
$818$		0			0
$819$	24619.1	+	8897.61i	1.05038	+	0.379619i
$820$		0			0
$821$	−16661.5	+	9619.52i	−0.708271	+	0.408920i	−0.810420	−	0.585849i	$-0.800761\pi$
$821$	−16661.5	+	9619.52i	−0.708271	+	0.408920i	0.102150	+	0.994769i	$0.467428\pi$
$822$		0			0
$823$	−987.266	+	1710.00i	−0.0418152	+	0.0724261i	−0.886176	−	0.463350i	$-0.846647\pi$
$823$	−987.266	+	1710.00i	−0.0418152	+	0.0724261i	0.844360	+	0.535776i	$0.179981\pi$
$824$		0			0
$825$	3299.57	−	461.309i	0.139244	−	0.0194676i
$826$		0			0
$827$		−	18657.5i		−	0.784506i	−0.919857	−	0.392253i	$-0.871696\pi$
$827$		−	18657.5i		−	0.784506i	0.919857	−	0.392253i	$-0.128304\pi$
$828$		0			0
$829$		−	39035.0i		−	1.63539i	−0.575650	−	0.817696i	$-0.695251\pi$
$829$		−	39035.0i		−	1.63539i	0.575650	−	0.817696i	$-0.304749\pi$
$830$		0			0
$831$	−40062.1	−	16219.6i	−1.67237	−	0.677079i
$832$		0			0
$833$	8866.88	−	9995.34i	0.368811	−	0.415748i
$834$		0			0
$835$	8472.04	+	14674.0i	0.351122	+	0.608161i
$836$		0			0
$837$	−2011.48	+	18749.4i	−0.0830668	+	0.774281i
$838$		0			0
$839$	7645.68	+	13242.7i	0.314610	+	0.544921i	0.979355	−	0.202150i	$-0.0647928\pi$
$839$	7645.68	+	13242.7i	0.314610	+	0.544921i	−0.664744	+	0.747071i	$0.731459\pi$
$840$		0			0
$841$	−10324.5	+	17882.6i	−0.423326	+	0.733223i
$842$		0			0
$843$	9062.30	−	22383.7i	0.370252	−	0.914514i
$844$		0			0
$845$	−3842.36			−0.156427
$846$		0			0
$847$	−23179.2	−	2349.61i	−0.940315	−	0.0953170i
$848$		0			0
$849$	−23591.4	+	3298.29i	−0.953659	+	0.133330i
$850$		0			0
$851$	51990.1	+	30016.5i	2.09424	+	1.20911i
$852$		0			0
$853$	−24102.9	+	13915.8i	−0.967486	+	0.558579i	−0.898469	−	0.439037i	$-0.855320\pi$
$853$	−24102.9	+	13915.8i	−0.967486	+	0.558579i	−0.0690174	+	0.997615i	$0.521986\pi$
$854$		0			0
$855$	−8816.72	+	9103.78i	−0.352661	+	0.364144i
$856$		0			0
$857$	−12190.5	−	21114.6i	−0.485905	−	0.841613i	0.513963	−	0.857812i	$-0.328177\pi$
$857$	−12190.5	−	21114.6i	−0.485905	−	0.841613i	−0.999869	+	0.0161994i	$0.994843\pi$
$858$		0			0
$859$	23886.7	+	13791.0i	0.948781	+	0.547779i	0.892702	−	0.450647i	$-0.148807\pi$
$859$	23886.7	+	13791.0i	0.948781	+	0.547779i	0.0560791	+	0.998426i	$0.482140\pi$
$860$		0			0
$861$	36050.1	−	22676.3i	1.42693	−	0.897566i
$862$		0			0
$863$		−	26388.4i		−	1.04087i	−0.853901	−	0.520436i	$-0.825770\pi$
$863$		−	26388.4i		−	1.04087i	0.853901	−	0.520436i	$-0.174230\pi$
$864$		0			0
$865$	−224.682			−0.00883171
$866$		0			0
$867$	−13911.2	+	10852.6i	−0.544925	+	0.425112i
$868$		0			0
$869$	−1490.41	−	860.490i	−0.0581804	−	0.0335905i
$870$		0			0
$871$	28919.4	−	16696.6i	1.12502	−	0.649532i
$872$		0			0
$873$	−145.956	−	511.782i	−0.00565850	−	0.0198410i
$874$		0			0
$875$	−10739.9	−	23884.1i	−0.414941	−	0.922775i
$876$		0			0
$877$	15753.5	−	27285.8i	0.606564	−	1.05060i	−0.385238	−	0.922817i	$-0.625881\pi$
$877$	15753.5	−	27285.8i	0.606564	−	1.05060i	0.991802	−	0.127782i	$-0.0407859\pi$
$878$		0			0
$879$	2821.95	+	20184.3i	0.108284	+	0.774517i
$880$		0			0
$881$	1153.83			0.0441243			0.0220621	−	0.999757i	$-0.492977\pi$
$881$	1153.83			0.0441243			0.0220621	+	0.999757i	$0.492977\pi$
$882$		0			0
$883$	22903.1			0.872877			0.436439	−	0.899734i	$-0.356240\pi$
$883$	22903.1			0.872877			0.436439	+	0.899734i	$0.356240\pi$
$884$		0			0
$885$	−13024.1	−	5272.97i	−0.494691	−	0.200281i
$886$		0			0
$887$	−14902.5	+	25811.9i	−0.564123	+	0.977090i	0.433008	+	0.901390i	$0.357452\pi$
$887$	−14902.5	+	25811.9i	−0.564123	+	0.977090i	−0.997131	+	0.0756994i	$0.975881\pi$
$888$		0			0
$889$	5881.57	+	13079.8i	0.221892	+	0.493458i
$890$		0			0
$891$	−6226.56	+	199.534i	−0.234116	+	0.00750239i
$892$		0			0
$893$	15834.7	−	9142.19i	0.593381	−	0.342589i
$894$		0			0
$895$	9507.58	+	5489.20i	0.355087	+	0.205010i
$896$		0			0
$897$	50629.9	+	20498.1i	1.88460	+	0.763001i
$898$		0			0
$899$	−8219.80			−0.304945
$900$		0			0
$901$		−	5322.64i		−	0.196807i
$902$		0			0
$903$	190.544	+	5026.95i	0.00702204	+	0.185256i
$904$		0			0
$905$	−21528.1	−	12429.2i	−0.790737	−	0.456532i
$906$		0			0
$907$	10173.5	+	17621.0i	0.372442	+	0.645089i	0.989941	−	0.141483i	$-0.0451872\pi$
$907$	10173.5	+	17621.0i	0.372442	+	0.645089i	−0.617499	+	0.786572i	$0.711854\pi$
$908$		0			0
$909$	−42285.6	+	12059.5i	−1.54293	+	0.440032i
$910$		0			0
$911$	26966.9	−	15569.4i	0.980740	−	0.566231i	0.0782466	−	0.996934i	$-0.475068\pi$
$911$	26966.9	−	15569.4i	0.980740	−	0.566231i	0.902494	+	0.430703i	$0.141735\pi$
$912$		0			0
$913$	−4787.55	−	2764.10i	−0.173543	−	0.100195i
$914$		0			0
$915$	−6827.69	−	8751.99i	−0.246685	−	0.316210i
$916$		0			0
$917$	14845.1	+	1504.81i	0.534600	+	0.0541909i
$918$		0			0
$919$	18807.6			0.675089			0.337545	−	0.941310i	$-0.390404\pi$
$919$	18807.6			0.675089			0.337545	+	0.941310i	$0.390404\pi$
$920$		0			0
$921$	−25679.8	−	32917.3i	−0.918760	−	1.17770i
$922$		0			0
$923$	5974.46	−	10348.1i	0.213057	−	0.369026i
$924$		0			0
$925$	11215.8	+	19426.3i	0.398674	+	0.690523i
$926$		0			0
$927$	13970.4	−	14425.3i	0.494982	−	0.511098i
$928$		0			0
$929$	13698.8	+	23727.0i	0.483791	+	0.837951i	0.999827	−	0.0186161i	$-0.00592603\pi$
$929$	13698.8	+	23727.0i	0.483791	+	0.837951i	−0.516035	+	0.856567i	$0.672593\pi$
$930$		0			0
$931$	−17037.7	−	15114.2i	−0.599773	−	0.532059i
$932$		0			0
$933$	−3187.92	−	22802.0i	−0.111863	−	0.800112i
$934$		0			0
$935$		−	2353.19i		−	0.0823075i
$936$		0			0
$937$			27022.7i			0.942149i	0.882093	+	0.471075i	$0.156134\pi$
$937$			27022.7i			0.942149i	−0.882093	+	0.471075i	$0.843866\pi$
$938$		0			0
$939$	11542.4	−	28509.4i	0.401141	−	0.990810i
$940$		0			0
$941$	−8024.19	+	13898.3i	−0.277982	+	0.481479i	−0.970883	−	0.239554i	$-0.922999\pi$
$941$	−8024.19	+	13898.3i	−0.277982	+	0.481479i	0.692901	+	0.721033i	$0.256332\pi$
$942$		0			0
$943$	76960.1	−	44432.9i	2.65765	−	1.53440i
$944$		0			0
$945$	5702.78	+	17459.6i	0.196309	+	0.601017i
$946$		0			0
$947$	−3053.61	+	1763.00i	−0.104782	+	0.0604962i	−0.551475	−	0.834191i	$-0.685935\pi$
$947$	−3053.61	+	1763.00i	−0.104782	+	0.0604962i	0.446693	+	0.894687i	$0.352602\pi$
$948$		0			0
$949$	−32501.2	+	56293.7i	−1.11173	+	1.92557i
$950$		0			0
$951$	1031.34	−	2547.39i	0.0351666	−	0.0868609i
$952$		0			0
$953$			31452.5i			1.06909i	0.845139	+	0.534547i	$0.179518\pi$
$953$			31452.5i			1.06909i	−0.845139	+	0.534547i	$0.820482\pi$
$954$		0			0
$955$			16088.5i			0.545142i
$956$		0			0
$957$	−376.003	−	2689.41i	−0.0127006	−	0.0908426i
$958$		0			0
$959$	27537.3	+	19851.9i	0.927244	+	0.668458i
$960$		0			0
$961$	−5862.71	−	10154.5i	−0.196795	−	0.340858i
$962$		0			0
$963$	21906.9	+	5495.42i	0.733062	+	0.183891i
$964$		0			0
$965$	5622.01	+	9737.61i	0.187543	+	0.324834i
$966$		0			0
$967$	4935.48	−	8548.51i	0.164131	−	0.284283i	−0.772215	−	0.635361i	$-0.780851\pi$
$967$	4935.48	−	8548.51i	0.164131	−	0.284283i	0.936346	+	0.351078i	$0.114185\pi$
$968$		0			0
$969$	−8267.18	−	10597.2i	−0.274076	−	0.351321i
$970$		0			0
$971$	9155.66			0.302594			0.151297	−	0.988488i	$-0.451655\pi$
$971$	9155.66			0.302594			0.151297	+	0.988488i	$0.451655\pi$
$972$		0			0
$973$	1650.94	−	16286.8i	0.0543954	−	0.536618i
$974$		0			0
$975$	12553.9	+	16092.1i	0.412357	+	0.528574i
$976$		0			0
$977$	11814.1	+	6820.88i	0.386865	+	0.223356i	0.680801	−	0.732469i	$-0.261632\pi$
$977$	11814.1	+	6820.88i	0.386865	+	0.223356i	−0.293936	+	0.955825i	$0.594965\pi$
$978$		0			0
$979$	−6113.31	+	3529.52i	−0.199573	+	0.115224i
$980$		0			0
$981$	−10275.1	+	40960.6i	−0.334413	+	1.33310i
$982$		0			0
$983$	28836.8	+	49946.9i	0.935659	+	1.62061i	0.773455	+	0.633851i	$0.218527\pi$
$983$	28836.8	+	49946.9i	0.935659	+	1.62061i	0.162203	+	0.986757i	$0.448140\pi$
$984$		0			0
$985$	−10503.1	−	6063.98i	−0.339754	−	0.196157i
$986$		0			0
$987$	−1003.72	−	26480.4i	−0.0323697	−	0.853982i
$988$		0			0
$989$			10496.7i			0.337489i
$990$		0			0
$991$	28668.4			0.918953			0.459476	−	0.888190i	$-0.348037\pi$
$991$	28668.4			0.918953			0.459476	+	0.888190i	$0.348037\pi$
$992$		0			0
$993$	17578.7	+	7116.93i	0.561774	+	0.227441i
$994$		0			0
$995$	15513.0	+	8956.44i	0.494267	+	0.285365i
$996$		0			0
$997$	3928.31	−	2268.01i	0.124785	−	0.0720448i	−0.436308	−	0.899797i	$-0.643714\pi$
$997$	3928.31	−	2268.01i	0.124785	−	0.0720448i	0.561093	+	0.827753i	$0.310381\pi$
$998$		0			0
$999$	−16977.6	−	38354.4i	−0.537684	−	1.21469i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.41.19	yes	48
3.2	odd	2		756.4.x.a.125.17		48
7.6	odd	2	inner	252.4.x.a.41.6	✓	48
9.2	odd	6	inner	252.4.x.a.209.6	yes	48
9.4	even	3		2268.4.f.a.1133.34		48
9.5	odd	6		2268.4.f.a.1133.15		48
9.7	even	3		756.4.x.a.629.8		48
21.20	even	2		756.4.x.a.125.8		48
63.13	odd	6		2268.4.f.a.1133.16		48
63.20	even	6	inner	252.4.x.a.209.19	yes	48
63.34	odd	6		756.4.x.a.629.17		48
63.41	even	6		2268.4.f.a.1133.33		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.6	✓	48	7.6	odd	2	inner
252.4.x.a.41.19	yes	48	1.1	even	1	trivial
252.4.x.a.209.6	yes	48	9.2	odd	6	inner
252.4.x.a.209.19	yes	48	63.20	even	6	inner
756.4.x.a.125.8		48	21.20	even	2
756.4.x.a.125.17		48	3.2	odd	2
756.4.x.a.629.8		48	9.7	even	3
756.4.x.a.629.17		48	63.34	odd	6
2268.4.f.a.1133.15		48	9.5	odd	6
2268.4.f.a.1133.16		48	63.13	odd	6
2268.4.f.a.1133.33		48	63.41	even	6
2268.4.f.a.1133.34		48	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +O(q^{10})\)	\(q+(4.09692 - 3.19613i) q^{3} +(-3.53447 + 6.12188i) q^{5} +(7.59538 + 16.8911i) q^{7} +(6.56950 - 26.1886i) q^{9} +(7.40072 - 4.27281i) q^{11} +(45.3367 + 26.1752i) q^{13} +(5.08588 + 36.3774i) q^{15} -38.9547 q^{17} +66.4008i q^{19} +(85.1039 + 44.9258i) q^{21} +(173.899 + 100.401i) q^{23} +(37.5151 + 64.9781i) q^{25} +(-56.7874 - 128.289i) q^{27} +(52.9622 - 30.5777i) q^{29} +(-116.401 - 67.2041i) q^{31} +(16.6637 - 41.1590i) q^{33} +(-130.251 - 13.2032i) q^{35} +298.967 q^{37} +(269.400 - 37.6645i) q^{39} +(221.278 - 383.265i) q^{41} +(26.1371 + 45.2708i) q^{43} +(137.104 + 132.780i) q^{45} +(-137.682 - 238.472i) q^{47} +(-227.620 + 256.589i) q^{49} +(-159.594 + 124.504i) q^{51} +136.637i q^{53} +60.4084i q^{55} +(212.226 + 272.039i) q^{57} +(-191.268 + 331.286i) q^{59} +(-261.714 + 151.100i) q^{61} +(492.253 - 87.9458i) q^{63} +(-320.482 + 185.030i) q^{65} +(318.940 - 552.420i) q^{67} +(1033.34 - 144.470i) q^{69} -228.249i q^{71} +1241.68i q^{73} +(361.375 + 146.307i) q^{75} +(128.384 + 92.5530i) q^{77} +(-100.694 - 174.407i) q^{79} +(-642.683 - 344.092i) q^{81} +(-323.452 - 560.235i) q^{83} +(137.684 - 238.476i) q^{85} +(119.251 - 294.549i) q^{87} -826.042 q^{89} +(-97.7786 + 964.598i) q^{91} +(-691.679 + 96.7027i) q^{93} +(-406.497 - 234.691i) q^{95} +(17.0700 - 9.85534i) q^{97} +(-63.2797 - 221.885i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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